%I #23 Feb 16 2025 08:33:30
%S 1,6,15,36,65,110,175,264,389,522,683,864,1077,1338,1615,1948,2293,
%T 2786,3307,3880,4457,5110,5783,6568,7377,8282,9291,10324,11321,12522,
%U 13715,15072,16461,18202,19763,21628,23441,25454,27443,29664,31821,34178,36571
%N Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 630", based on the 5-celled von Neumann neighborhood.
%C Initialized with a single black (ON) cell at stage zero.
%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H N. J. A. Sloane, <a href="http://arxiv.org/abs/1503.01168">On the Number of ON Cells in Cellular Automata</a>, arXiv:1503.01168, 2015
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t rule=630; stages=300; ca=CellularAutomaton[ {rule,{2,{{0,2,0},{2,1,2},{0,2,0}}},{1,1}}, {{{1}},0}, stages]; (* Start with single black cell *) on=Map[Function[Apply[Plus,Flatten[#1]]],ca]; (* Count ON cells at each stage *) Table[Total[Part[on,Range[1,i]]],{i,1,Length[on]}]
%Y Cf. A269523.
%K nonn,easy,changed
%O 0,2
%A _Robert Price_, Mar 01 2016